So this may sound a little weird, but my problem is that every time I start Chromium I have to login everywhere again (Facebook, Gmail etc.) no matter when I last logged in the last time.

I turn on my computer and start Chromium (it now asks me to unlock my keyring) and I start Facebook and I'm asked to log in. When closing Chromium now and starting it again I have to login again.

I'm using Ubuntu 12.04 64-bit, on my laptop I'm using Ubuntu 12.04 32-bit and the same version of Chromium and there's no problem like that. The main difference I figured is that when shutting down Chromium on my laptop, some chromium-browser processes keep running in the background which don't on my new PC.